New Insights in the Study of Pyrene Excimer Fluorescence to

Invited Feature Article pubs.acs.org/Langmuir

New Insights in the Study of Pyrene Excimer Fluorescence to Characterize Macromolecules and their Supramolecular Assemblies in Solution Jean Duhamel Institute of Polymer Research, Waterloo Institute for Nanotechnology, Department of Chemistry, University of Waterloo, Waterloo ON N2L 3G1, Canada ABSTRACT: This report highlights some of the recent developments that have been made in the quantitative analysis of fluorescence decays acquired with pyrene-labeled macromolecules. With these new analytical tools, macromolecules of different composition and architecture can now be labeled in a variety of ways with the pyrene chromophore, and the kinetics of pyrene excimer formation can be described to retrieve quantitative information about the internal dynamics of the macromolecules studied. In particular, this review presents the procedure that was followed to develop these new analytical tools and how the process of pyrene excimer formation with vinyl polymers, poly(L-glutamic acid), dendrimers, associative polymers, surfactants, and lipids labeled with pyrene has been successfully characterized thanks to these analysis programs.

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INTRODUCTION The study of the process of excimer formation between an excited-state and a ground-state pyrene covalently attached to a macromolecule has provided a wealth of dynamic and structural information on macromolecules in solution, whether they be short alkyl chains1 or low2 and large3 molecular weight linear polymers, dendritic macromolecules,4 and their assemblies as polymeric5 or surfactant micelles,6 or lipid vesicles,7 to name but a few applications. Contrary to most other techniques such as nuclear magnetic resonance, electron paramagnetic resonance, and fluorescence anisotropy that provide information on the internal dynamics of macromolecules via the rotational diffusion undergone by selected units of a macromolecule, excimer formation between pyrene labels covalently attached to a macromolecule stands out because it yields information about the translational diffusive motion of the units bearing the fluorescent labels. This advantageous feature provides straightforward answers about the internal dynamics of macromolecules, as illustrated when dealing with a fluorescently end-labeled rigid macromolecule such as a DNA duplex or a helical polypeptide. The dyes always retain some level of mobility with respect to the macromolecule as determined from their correlation times obtained by fluorescence anisotropy yet would never encounter via translational diffusion probed by pyrene excimer formation due to the inherent rigidity of the macromolecule. The variety and complexity of macromolecules that could be investigated by monitoring the process of pyrene excimer formation was captured by Winnik’s thorough 1993 review on the photophysics of preassociated pyrenes,5 which highlighted two major facts. First, the process of pyrene excimer formation could be used to gain detailed information on the © 2012 American Chemical Society

dynamics and structure of an apparently limitless variety of complex macromolecules and their supramolecular assemblies. Second, the vast majority of studies on pyrene-labeled macromolecules yielded only qualitative information on the process of pyrene excimer formation and, consequently, their dynamics and structure. Indeed, in these early days quantitative information on the kinetics of the formation of excimers between pyrene pendants covalently attached to a macromolecule could be obtained under the sole condition that the macromolecule be labeled with two and only two pyrenyl groups that would be separated by a single chain length.2 The untold general consensus was that any pyrene-labeled macromolecule whose design would not comply with this strict requirement could be studied only qualitatively. Over the past 15 years, my laboratory has made a number of advances in the analysis of the fluorescence decays obtained with pyrene-labeled macromolecules to characterize the dynamics and structure of macromolecules of varied size, composition, and architecture that can be pyrene-labeled at more than two specific positions. In effect, this review will argue that the field has reached a tipping point where quantitative information on the dynamics and structure of any pyrenelabeled macromolecule can now be obtained as long as some pyrene excimer formation occurs by diffusion and the macromolecule of interest is not constituted of building blocks such as secondary or tertiary amines that are inherent Received: December 2, 2011 Revised: February 28, 2012 Published: March 16, 2012 6527

dx.doi.org/10.1021/la2047646 | Langmuir 2012, 28, 6527−6538

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Invited Feature Article

quenchers of the pyrene monomer and/or excimer fluorescence.

encounter with a ground-state pyrene results in pyrene excimer formation. In this respect, pyrene excimer formation contrasts with other photophysical processes used to probe macromolecules such as electron transfer (ET)11 or fluorescence resonance energy transfer (FRET)12,13 where the excess energy of an excited donor can be transferred to an acceptor over a range of distances. Quenching of the excited donor by ET or FRET requires that the distribution of distances between donors and acceptors be determined and ensemble-averaged for every time interval of the fluorescence decay of the excited donor as is being done to probe polymer diffusion between latex particles.14 These mathematical considerations are irrelevant for pyrene excimer formation where quenching of the excited pyrene via excimer formation occurs only upon contact between two pyrenyl units. Compared to other excimer-forming fluorophores such as naphthalene, which easily undergoes energy migration,15 forms few excimers,16 and does so with a large dissociation rate constant,16,17 the unusual retention of excess energy by the pyrene chromophore is a consequence of the absence of overlap between its absorption and fluorescence spectra (Figure 1). Because the S10 ← S00 transition is symmetry-forbidden for pyrene,18 the molar absorption coefficient of pyrene is very small at the wavelengths where pyrene fluoresces, minimizing the chance of FRET or energy migration between pyrene molecules. Pyrene has two other properties that make it particularly attractive for the study of pyrene-labeled macromolecules by time-resolved fluorescence. Pyrene and its derivatives possessing at least one methylene unit in the 1-position have a long natural lifetime τM of several hundreds of nanoseconds, reaching 350 ns for an ethylene-propylene copolymer labeled with 1-pyrenemethylsuccinimide in hexane.10 The long lifetime of pyrene provides a well-suited temporal window for studying the internal dynamics of many macromolecules that take place on timescales that can range from the subnanosecond to the millisecond. Furthermore, pyrene possesses a large quantum yield and molar absorption coefficient for the S20 ← S00 transition (∼40 000 M−1·cm−1 at ∼344 nm depending on the pyrene derivative and solvent), which enable easy detection at submicromolar pyrene concentrations. At such low concentrations and if both the macromolecule and pyrenyl label are well-solvated, an excited pyrene label covalently attached to a macromolecule decays to the ground state before forming an excimer intermolecularly with a ground-state pyrene attached to a different macromolecule. In effect, the quantitative information retrieved for the dynamics and structure of the pyrene-labeled macromolecule by conducting time-resolved fluorescence measurements under these conditions reflects the properties of isolated macromolecules in solution, a feature matched by very few other techniques in a similar concentration regime of typically less than 10 mg·L−1 pyrenelabeled macromolecules. How these interesting properties can be harnessed to study pyrene-labeled macromolecules in solution by time-resolved fluorescence requires the implementation of analysis programs that are based on kinetic models whose derivations will be described after the following short historical review.

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PYRENE EXCIMER FORMATION The kinetics of excimer formation for pyrene-labeled macromolecules is well described by a modified version of the original Birks′ scheme.2,8,9 Upon absorption of a UV photon at around 340 nm, an excited pyrene can either fluoresce with its natural lifetime τM or form an excimer upon encountering a groundstate pyrene. The rate “constant” of excimer formation is given by the function f(t), which actually depends on time for most pyrene-labeled macromolecules and will be the topic of a more detailed discussion later in this review. The excimer can fluoresce with its natural lifetime τE0 or dissociate with a rate constant k−1. Except for pyrene end-labeled linear chains where the pyrene groups are well separated,2 a non-negligible fraction of pyrene groups often get incorporated next to each other in macromolecules and form excimers instantaneously upon excitation.10 These processes are depicted in Scheme 1. Scheme 1. Excimer Formation between Pyrenyl Groups Covalently Attached to a Macromolecule

Excimer formation can be readily probed by fluorescence as illustrated in Figure 1, which presents the fluorescence spectra of two solutions in tetrahydrofuran containing the same 2.5 × 10−6 M concentration of pyrenyl units. The 2K poly(ethylene oxide) chain labeled at both ends with a 1-pyrenemethoxy unit (PEO(2K)-Py2) forms an excimer that emits at 480 nm whereas 1-pyrenemethanol (PyMeOH) does not at so dilute a concentration. One of the key features of Scheme 1 is that after the absorption of a photon by a ground-state pyrene the energy remains localized on the excited pyrene monomer until

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INTERNAL DYNAMICS OF MACROMOLECULES PROBED BY PYRENE EXCIMER FORMATION In 1963, Birks demonstrated that excimer formation for molecular pyrene in solution was a reversible process that involved one rate constant for excimer formation (f(t) = k1 in

Figure 1. Molar absorbance coefficient spectrum of 1-pyrenemethanol (left) with the fluorescence spectra (right) of 1-pyrenemethanol in THF and a 2K poly(ethylene oxide) doubly labeled with 1-pyrene methanol. λex = 344 nm, [Py] = 2.5 × 10−6 M, solvent = tetrahydrofuran. Spectra were acquired by Shaohua Chen. 6528


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Furthermore, the early work carried out by Zachariasse on pyrene-labeled alkanes20,21,23 suggested that pyrene-labeled macromolecules forming excimers with more than two rate constants of excimer formation would exhibit kinetics that would be difficult to handle with the compartmental analysis.22,28 Because very few macromolecules other than linear chains have a chemical structure that lends itself to such a labeling scheme, the scientific community held the view that no quantitative information on the internal dynamics of macromolecules could be obtained if the macromolecules were labeled with more than two labels and if these two labels were not separated by a fixed chain length. Another consequence of the kcy ≈ N−1.6 relationship was that the efficiency of pyrene excimer formation (i.e., the events providing information on the internal dynamics of the pyrene-labeled macromolecule) decreased to vanishingly small levels as N increased. For instance, increasing N for a polystyrene construct from 30 to 300 styrene monomers would decrease kcy by 97%. In practice, kcy could be determined quantitatively from the analysis of fluorescence decays for short PS-Py2 constructs no longer than 100 styrene monomers.2,27 Thus, the two pyrene labels needed to be located not only at two specific positions on the macromolecule but also relatively close to each others. Such requirements were stringent and extremely cumbersome because most macromolecules could not be labeled in such a manner. According to the author, the main complication to solving the complex kinetics of pyrene excimer formation involving a distribution of excimer formation rate constants resides in the excimer dissociation because each dissociated excimer yields an excited pyrene that can reform an excimer with another ground-state pyrene according to another distribution of rate constants. The dissociation of the excimer at random times, followed by the reformation of the excimer according to a distribution of rate constants, is difficult to handle mathematically, although it has been achieved in a few instances using a convolution procedure.29,30 However, although k−1 exists and has been shown to be non-negligible for some short pyrene end-labeled alkanes where pyrene is directly linked to the chain without heteroatoms, as for 1,3-di(1-pyreny)propane,31 many experiments carried out on pyrene excimer formation indicate that k−1 is small at room temperature,2,8,21,29 leading to question whether it should be considered at all, at least in the study of pyrene-labeled macromolecules. This question was answered indirectly in 1995 when Yekta et al. used pyrene excimer formation in micelles generated by hydrophobically modified ethoxylated urethane polymers (HEUR) to determine the aggregation number (Nagg) of the HEUR micelles.32 In these experiments, the fluorescence decays of the pyrene monomer were fitted successfully by assuming that all pyrenes were distributed among the HEUR micelles according to a Poisson distribution, that the pyrene excimer was formed with a distribution of rate constants, and that pyrene excimer dissociation was negligible.33 The reasonable kinetic parameters and Nagg values retrieved by assuming k−1 = 0 s−1 in the HEUR study32 suggested that the assumption of k−1 = 0 s−1 could also be applied to other cases when the pyrene excimer is formed according to a distribution of rate constants. How this insight was taken advantage of to develop new analyses to describe the process of excimer formation in a wide variety of pyrene-labeled macromolecules is described hereafter.

Scheme 1) and one rate constant for excimer dissociation (k−1).19 In 1976, Zachariasse used steady-state fluorescence to study the efficiency of intramolecular excimer formation between two pyrene units covalently attached to the ends of an alkyl chain.1 Because the pyrene units were covalently attached to the alkyl chain, excimer formation provided information on the ring closure process of the alkyl chain. The kinetics of excimer formation were found to be much more complex for these pyrene-labeled alkanes than for pyrene solutions in organic solvents,8,19 typically involving three exponentials and, consequently, three excited species (one monomer and two excimers in the case of pyrene derivatives substituted in the 1-position) that interacted with one another by the reversible dissociation and reformation of the pyrene excimers.20,21 The differential equations describing the kinetics of pyrene excimer formation for these constructs could be solved according to the compartmental analysis22 of the fluorescence decays with a 3 × 3 matrix.23 However, the large number of rate constants involved (two rate constants for excimer formation and two rate constants for excimer dissociation in the DMD model) required additional information to be provided in order to retrieve all rate constants quantitatively. These studies conveyed the impression that the mathematical handling of more than two rate constants for pyrene excimer formation would be quasi-impossible via compartmental analysis. Following theoretical work carried out by Wilemski and Fixman in 1974 that demonstrated that end-to-end cyclization (EEC) for monodisperse polymers should be described by a single rate constant kcy,24,25 the idea of using pyrene excimer formation to study the EEC of oligomers was extended in 1977 by Cuniberti and Perico to a series of monodisperse poly(ethylene oxide)s end labeled with 1-pyrenebutyrate ester groups (PEO-Py2).26 The steady-state fluorescence spectra of the PEO-Py2 solutions in tetrahydrofuran showed a decrease in the ratio of the steady-state (SS) fluorescence intensity of the excimer over that of the monomer, namely, the (IE/IM)SS ratio, with increasing chain length, a consequence of the decrease in EEC events between pyrene end groups as they are held away from one another by a longer chain. However, the demonstration by Winnik et al. in 1980 in which an analysis of the fluorescence decays of a series of monodisperse polystyrenes end-labeled with pyrene (PS-Py2) according to Birks′ scheme (Scheme 1 with f(t) = kcy) quantitatively yielded the EEC rate constant kcy illustrated the importance of conducting time-resolved fluorescence measurements to probe the internal dynamics of pyrene-labeled macromolecules.27 However, in a curious twist of fate, the exciting developments enabled by Winnik’s experiments on pyrene endlabeled monodisperse polymers2,27 led the quantitative characterization of the internal dynamics of macromolecules through the study of pyrene excimer formation to a dead end. Indeed, an important result obtained by Winnik was to establish that kcy depends strongly on the polymer chain length N and scales as N−1.6 for PS-Py2 in cyclohexane at 34.5 °C.27 Although this was an important result in polymer science, it also indicated that the condition f(t) = ⟨k1⟩, where ⟨k1⟩ represents a unique average rate constant of excimer formation, would be obtained only if a macromolecule were to be labeled with pyrene at two specific positions. More than two labels per macromolecule would introduce a distribution of distances between them that would result in a distribution of rate constants that could not be handled by Birks′ scheme. 6529


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With an expression for [Pydiff * ](t) at hand, f(t) can be determined according to eq 4, which is obtained by rearranging eq 1 with the assumption k−1 = 0.

MODELING THE PROCESS OF PYRENE EXCIMER FORMATION

On the basis of Scheme 1, two differential equations can be derived that describe the kinetic constraints to which the concentration of the excited pyrene monomer forming the excimer by diffusion, Pydiff * , and the excimer, E0*, are being subjected to. They are given in eqs 1 and 2 by assuming that the solution is irradiated with a short pulse of light. d[Py *diff ] dt

d[Py *diff ]

1 [Py *diff ] dt τM n ⎛1 1 ⎞ * = [Py diff ](t = 0) × ∑ ai⎜ − ⎟ × exp( −t /τi) τM ⎠ ⎝ τi i=1

f (t ) = −

−

(4)

= − f (t ) −

1 [Py *diff ] + k−1[E 0*] τM

d[E 0*] 1 = f (t ) − [E 0*] − k−1[E 0*] dt τE0

The f(t) expression allows the integration of eq 2, whose solution is trivial because f(t) can always be expressed as a sum of exponentials and is given in eq 5 where f(t) has been replaced by the function fo(t) = f(t)/[Pydiff * ](t=0).

(1)

∫

× exp(u/τE) du] × exp(−t /τE)

Equations 1 and 2 are two first-order differential equations that are coupled through the rate of excimer formation (f(t)) and excimer dissociation (k−1). In the case where excimer formation can be described by a single rate constant (⟨k1⟩) such as for the cyclization of pyrene end-labeled monodisperse linear polymers (i.e., two pyrene labels per macromolecule separated by a welldefined chain length),2,27 Birks managed to find an exact expression for the time-dependent concentrations [Pydiff * ](t) and [E0*](t).8,19 Unfortunately, for any other case where f(t) cannot be approximated by the product ⟨k1⟩ × [Pydiff * ](t), the integration of eqs 1 and 2 is not straightforward and requires assumptions to be made. The basic assumption made by this laboratory is that k−1 is negligible at room temperature, as was done to characterize the HEUR micelles,32 a fact supported by numerous studies conducted in particular with pyrene end-labeled polymers.2,27,29,34 The assumption that k−1 is negligible justifies the removal of the term k−1 × [E0*] in eqs 1 and 2 and, most importantly, unlinking the effect that the behavior of the function [E0*](t) might have on [Pydiff * ](t). This leads to the fundamental postulate on which all derivations made by this * ](t) can be laboratory are based, namely, that the function [Pydiff handled independently of [E0*](t). In practice, prior knowledge of the macromolecule guides the experimentalist in deriving an expression for [Pydiff * ](t) that captures the main features expected from the macromolecule. The expression of [Pydiff * ](t) is used to determine f(t), which is then applied to integrate eq 2 to yield [E0*](t). In the most extreme but also simplest possible derivation, no assumption needs to be made about the way that [Pydiff * ](t) decays:35 [Pydiff * ](t) can be assumed to decay as a sum of exponentials as shown in eq 3, where ai and τi are the preexponential factors and decay times, respectively. The ai preexponential factors are normalized so that ∑in= 1 ai = 1.

1 1 − τ τM [E 0*](t ) = − [Py *diff ](t = 0) × ∑ ai 1i exp( −t /τi) 1 − i=1 τ τE 0 i

⎛ n ⎜ +⎜[E 0*](t = 0) + [Py *diff ](t = 0) × ∑ ai ⎜ i=1 ⎝

1 1 − τi τM 1 1 − τi τE 0

× exp( −t /τE 0)

⎞ ⎟ ⎟ ⎟ ⎠ (5b)

Equation 5b might appear complicated, but it is a simple sum of exponentials similar to many others commonly used in the literature.2,8,20,21,23,36−38 Furthermore, parameters ai and τi are the same as those employed in eq 3. The procedure described above was first introduced in 2005,35 and because it made no assumption on how [Pydiff * ](t) decays, it has been coined the model free (MF) analysis.39 Other expressions of [Pydiff * ](t) that have been introduced by this laboratory are based on the sequential model (SM),40 the fluorescence blob model (FBM),3 and a combination of the FBM and the SM models.41,42 The expressions for [Pydiff * ](t) and [E0*](t) that are obtained by applying the protocol outlined above assume that each Pydiff * species fluoresces or forms an excimer and that the excimer emits with a lifetime of τE0. Unfortunately, such clear-cut conditions are rarely obtained with pyrene-labeled macromolecules. Often, some of the pyrene labels are located in pyrene-poor regions of the macromolecule where they cannot form an excimer and they emit as free pyrenes. A residual unattached pyrene label might be present in the sample if the purification following the pyrene labeling step is not sufficiently thorough. These pyrene species that emit as if they were free in solution are taken into account by adding the contribution [Pydiff * ](t) given in eq 6 to the expression for [Pydiff * ](t).9 [Py *free](t ) = [Py *free](t = 0) × exp(−t /τM)

(6)

Furthermore, the crowded interior of the macromolecule often hinders the motions of the pyrene labels so that dimers are being formed with pyrene pendants that are poorly stacked. Upon direct excitation, these dimers (D*) emit with a lifetime of τD that can be longer or shorter than τE0. Species D* are

∑ ai × exp(−t /τi) i=1

(5a)

n

n

[Py *diff ](t ) = [Py *diff ](t = 0) ×

t

[E 0*](t ) = [[E 0*](t = 0) + [Py *diff ](t = 0) f (u) t=0 o

(2)

(3) 6530


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assumed to be generated by either direct excitation, in which case eq 7 needs to be added to eq 5,35,41 or diffusion, in which case eq 5 needs to be duplicated by replacing τE0 with τD.43 [D*](t ) = [D*](t = 0) × exp( −t /τD)

(7)

1 1 − τi τM bi = ai × 1 1 − τi τE 0

∞

t=0

⎤

t

∫t = 0 ⎢⎣∫u = 0 fo (u) exp(u/τE0) du⎥⎦

⎫ ⎪ exp( −t /τE 0) dt + fE 0 τE 0 + fD τD⎬ ⎪ ⎭ ⎧ ∞⎡ t ⎪ ⎤ fo (u) exp(u/τM) du⎥ /⎨fdiff (τM − ⎢⎣ ⎦ t=0 u=0 ⎪ ⎩

∫

∫

⎫ ⎪ exp( −t /τM) dt ) + ffree τM⎬ ⎪ ⎭

(9)

Unfortunately, this condition is typically quite difficult to fulfill because parameters ai, bi, τi, and τE0 are optimized not so that their values obey eq 9 but rather to optimize the fit of the fluorescence decays. To address this issue, an important contribution from this laboratory was to recognize that the pre-exponential factor bi is not a simple scalar but rather a function of parameters ai, τi, and τE0 and that its value should be optimized according to the parameters of which it is a function. The implementation of these considerations complicates the writeup of the analysis programs by substantially lengthening the sections of the programs that deal with the optimization of the various parameters. However, this complication in programming represents a small price to pay considering the numerous benefits associated with its implementation. The first obvious benefit associated with the application of this procedure is that eq 9 is always obeyed. The second one is that the number of floating parameters is reduced because the pre-exponential factors bi are no longer needed in the optimization, which explains why the parameters describing the kinetics of pyrene excimer formation are recovered with improved accuracy. The third advantage is that molar fractions fdiff, f free, f E0, and f D describing the different pyrene species present in solution are readily obtained in a quantitative manner from the analysis of the decays. The fourth and last advantage is the ability to calculate the (IE/IM)SPC ratio, which is an absolute measure of the (IE/IM)SS ratio. (See eq 8.) It is important to note that none of the advantages listed above can be attained in as straightforward a manner if the decay times and pre-exponential factors of the equations used to represent the pyrene monomer and excimer are not optimized as a function of the parameters that describe the

∫ = 0 [E*](t ) dt ⎛ IE ⎞SPC = t∞ ⎜ ⎟ ⎝ IM ⎠ ∫ [Py*](t ) dt ∞⎡

ANALYSIS PROGRAMS

Equations describing the time-dependent concentration profile of a pyrene monomer and excimer can always be written as the sums of exponentials of the type shown in eqs 3 and 5b.2,8,20,21,23,36−38 The main difference between the different expressions proposed in the literature resides in the physical interpretation of the pre-exponential factors and decay times used in the sums of exponentials. The difficulties associated with the recovery of decay times and pre-exponential factors are well documented for the analysis of fluorescence decays with sums of exponentials.47 Analyses of fluorescence decays requiring more than two exponentials with well-separated decay times cannot usually differentiate between different complex models.48 A key improvement in the analysis programs was achieved by linking the exponentials that are the same in the equations describing the monomer and excimer decays through the global analysis of the monomer and excimer decays.20,49,50 This refinement improved the quality of the recovery of the decay times, but the interpretation of the preexponential factors was still plagued by the following problem, which is illustrated by taking the equations derived for the MF analysis as a specific example. Considering eq 5b for the excimer decay, although the pre-exponential factor bi of the exponential exp(−t/τi) would be fitted as a simple scalar, parameters ai, bi, τi, and τE0 retrieved from the global analysis of the fluorescence decays are expected to obey eq 9.

Information about the kinetics of pyrene excimer formation and consequently the internal dynamics of the macromolecule to which the pyrene labels are covalently attached is retrieved from the parameters used to build the function [Pydiff * ](t), whether they are the pre-exponential factors ai and decay times τi for the MF analysis,9,35,39,43 the number of units constituting a blob and the rate constant for excimer formation inside a blob for the FBM,3 or the rate constants describing the diffusive encounters between two polymer units bearing a pyrene label followed by their rapid rearrangement in the SM.40−42 An analysis of the pyrene monomer and excimer fluorescence decays with equations based on the protocol outlined earlier also provides the molar fractions of the pyrene pendants present in the macromolecule as Pydiff * ( fdiff), Pyfree * ( f free), E0*( f E0), and D*( f D).9,10,35,39−46 In turn, these molar fractions can be used to characterize the distribution of pyrene labels on the macromolecule. For instance, the nonzero sum fagg = f E0 + f D indicates that pyrene aggregates are present because of the clustering10 or poor solvency of the pyrene pendants.44,45 A large f free value reflects a stiff macromolecule where a large number of pyrene pendants do not form excimers.46 Finally, the analyses presented herein yield the ratio of the fluorescence intensity of the pyrene excimer over that of the pyrene monomer, namely, the (IE/IM)SPC ratio where the subscript SPC indicates that the ratio has been obtained by using parameters retrieved from the analysis of the fluorescence decays.9,35,37−39,43 As such, the (IE/IM)SPC ratio represents an absolute quantity that is independent of the time-resolved fluorometer used. Its expression is given in eq 8.

⎧ ⎪ = ⎨fdiff ⎪ ⎩


(8)

In this laboratory, eq 8 proved to be quite useful in determining the effect that the presence of unattached pyrene labels had on the ratio (IE/IM)SS obtained for pyrene-labeled macromolecules by steady-state fluorescence.9,39 This was achieved by setting SPC f free equal to zero in eq 8 to obtain (IE/IM)free = 0 and monitoring the difference between (IE/IM)freeSPC= 0 and (IE/IM)SPC. How the equations described in this section are incorporated into the analysis programs that were developed to fit the pyrene monomer and excimer decays is illustrated hereafter. 6531


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Figure 2. (Left) Chemical structure of the pyrene-labeled polystyrene constructs. (Right) Plots of the products kblob × Nblob and kcy × N (top) before and (bottom) after normalization as a function of the inverse solvent viscosity.42,55

excited pyrene will have emitted as an isolated pyrene with its natural lifetime τM. The blob defines the volume probed by the excited pyrene, which depends on the flexibility of the polymer backbone. The blob can be used as a unit volume to divide the polymer coil into a cluster of blobs among which the pyrene labels distribute themselves randomly according to a Poisson distribution. In such a situation, the kinetics of pyrene excimer formation are similar to those encountered in surfactant micelles,33 with the only difference being that where micelles have well-defined boundaries the blobs remain a pure product of our imagination with virtual boundaries that fluctuate according to the backbone flexibility,53 solvent viscosity,54,55 or pyrene lifetime,56,57 which depends on the pyrene derivative and solvent.42,56 Equations were derived that yield kblob, the rate constant of excimer formation inside a blob containing one excited pyrene and one ground-state pyrene, and Nblob, the number of monomer units constituting the polymer segment occupying a blob.52 To date, the applicability of the FBM analysis has been demonstrated for a number of polymeric backbones randomly labeled with pyrene such as polystyrene,52,54,55,57 poly(N,N-dimethylacrylamide),58,59 polyisoprene,53 poly(L-glutamic acid),56,60 and poly(N-isopropylacrylamide).41 Although monomer and excimer fluorescence decays acquired with polymers randomly labeled with pyrene could be analyzed quantitatively with the FBM, these studies still did not demonstrate that the FBM analysis retrieved parameters that described the internal dynamics of a macromolecule. This conclusion was reached in 2008 by comparing the products kblob × Nblob and kcy × N obtained with polydisperse

kinetics of pyrene excimer formation. In this laboratory, this protocol has been implemented to analyze the fluorescence decays according to the classic Birks′ scheme, the FBM, the SM, and the MF analysis.

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EXAMPLES OF APPLICATIONS Fluorescence Blob Model. One example where pyrene excimer formation occurs according to a distribution of rate constants is for polymers randomly labeled with pyrene. In such macromolecules, each pyrene pair is separated by a unique polymer chain length that yields an excimer rate constant. The infinite number of possible pyrene pairs found along the polymer yields an infinite number of excimer formation rate constants, which greatly complicates the analysis of their fluorescence decays.51 A solution to this problem was proposed in 1999 by introducing a fluorescence blob model (FBM) to study macromolecules randomly labeled with pyrene.52 The FBM acknowledges that during the few hundreds of nanoseconds that it remains excited an excited pyrene attached to a macromolecule cannot probe the entire volume occupied by the macromolecule but rather a subvolume referred to as a blob. This conclusion was reached by considering that for a diffusive encounter to occur between an excited-state and a ground-state pyrene, a pyrene label must drag the chain behind it and weave its way through the polymeric segments constituting the macromolecule and still be excited when it encounters the ground-state pyrene. If the excited pyrene has returned to the ground-state before encountering the groundstate pyrene, then no excimer will be formed and the no longer 6532


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kinetics of pyrene excimer formation for the PEO-Py 2 constructs that were retrieved by Birks′ scheme analysis of the fluorescence decays was not physically meaningful. An analysis of the fluorescence decays obtained with the PEO-Py2 constructs with a version of the FBM adapted to pyrene endlabeled polymers yielded a set of kinetic parameters that were consistent with the FBM fundamentals. In particular, the blob radius could be determined and was found to increase with decreasing solvent viscosity. This study34 demonstrated that the FBM is an important analytical tool for studying the internal dynamics of linear chains whether they are randomly labeled or end labeled with pyrene. Model Free Analysis. Although the FBM was instrumental in providing a theoretical framework for analyzing the fluorescence decays of polymers randomly labeled or end labeled with pyrene, it still could not handle macromolecules that were pyrene labeled at more than two specific positions. This was unfortunate because this situation prevented the study of the internal dynamics of dendrimers.4 Dendrimers constitute a vast family of macromolecules that are endowed with numerous specific labeling sites, namely, their terminal ends.62 By the nature of their cascade synthesis, dendrimers are treelike macromolecules with branches of well-defined length terminated with a reactive group that can be easily labeled with a fluorophore such as pyrene. Because labeling dendrimers at the chain ends corresponds to a specific labeling, the FBM3 does not apply because the labels are not randomly attached to the macromolecule. Because the dendrimers have more than two ends, Birks′ scheme analysis2 does not apply either because more than two pyrene labels are attached to the macromolecule. The model free (MF) analysis35 was introduced to handle the complex kinetics of excimer formation for any type of pyrene-labeled macromolecule, including pyrene-labeled dendrimers. It was applied to analyze the fluorescence decays of a series of four poly(2,2-bis(hydroxymethyl)-propionic acid) dendrimers of generations one through four labeled with 1pyrenebutyl groups.39 As for any dendritic macromolecules, the local concentration of pyrene-labeled ends inside the dendrimer volume, and thus the local pyrene concentration [Py]loc, was very large, which, when combined with the flexible polymeric scaffold of the dendrimer, afforded efficient excimer formation. In turn, efficient excimer formation was accompanied by a strong quenching of the excited pyrene monomer, which made these experiments extremely sensitive to the unavoidable presence of residual unattached pyrene labels. In the case of the fourth-generation dendrimer labeled with 16 pyrenyl groups (Py16-G4), the presence of 3 mol % unattached pyrene labels was found to reduce the (IE/IM)SS and (IE/IM)SPC ratios by no less than 75%! The true value of the (IE/IM)SPC ratio was obtained by setting f free equal to zero in eq 8 to yield (IE/ SPC , which was 4 times larger than (IE/IM)SPC. The IM)free=0 separation of the unattached pyrenyl label by gel permeation chromatography yielded the pure Py16-G4 sample and an (IE/ SPC obtained for the crude Py16IM)SPC ratio similar to (IE/IM)free=0 G4 sample. MF analysis of the fluorescence decays acquired for the four SPC pyrene-labeled dendrimers yielded a set of (IE/IM)free=0 ratios and average rate constants of excimer formation () that were internally consistent and increased linearly with increasing SPC generation number (Figure 3). Because (IE/IM)free=0 and ⟨k⟩ depend on the local concentration of pyrene inside the dendrimers [Py]loc, the trends obtained with these quantities suggested that [Py]loc also increased linearly with the

polystyrenes randomly labeled with pyrene and linear monodisperse polystyrenes end labeled with pyrene, respectively.55 Rate constants kblob and kcy are two pseudounimolecular rate constants that are products of a bimolecular rate constant k1 describing the diffusive encounters between two pyrene labels covalently attached to a polymer and the local concentration equivalent to one ground-state pyrene inside a blob (1/Vblob) and inside a polymer coil (1/Vcoil), respectively. Consequently, the products kblob × Nblob and kcy × N are expected to be quantities that are equivalent to the product of k1 and the local polymer concentration inside a blob and the polymer coil, respectively. When the products kblob × Nblob obtained for three series of polystyrenes randomly labeled with different pyrene derivatives and kcy × N obtained for three polystyrene constructs end labeled with 1-pyrenebutylamine in nine different solvents were plotted as a function of the inverse solvent viscosity, four different trends were obtained that reflected the differences in the method used to label the polymers (Figure 2).42,55 However, all trends merged into a single one after normalization, demonstrating that the analysis of the fluorescence decays acquired with pyrene-labeled polystyrene yielded the same information on polymer chain dynamics regardless of whether the chain was polydisperse and randomly labeled with pyrene or monodisperse and end labeled with pyrene. Figure 2 demonstrates that the product kblob × Nblob is inversely proportional to the solution viscosity as expected for a diffusion-controlled process, a result that had been established for kcy by Winnik using a 9.6K sample of a pyrene end-labeled monodisperse poly(ethylene oxide).61 Since then, similar conclusions have been reached with pyrenelabeled poly(N-isopropylacrylamide).41 Furthermore, pyrene excimer formation was found to be dramatically enhanced when dealing with randomly labeled polymers because the pyrene labels were not held apart from each other, as was the case for end-labeled polymers.41,55 Finally, it was also noted that much simpler synthesis skills are required to prepare a polydisperse randomly labeled polymer. Together, these results suggested that the study of polymer chain dynamics in solution carried out with pyrene-labeled polymers would benefit considerably from attaching the pyrene labels randomly onto the polymer backbone instead of the ends of monodisperse chains. Because the FBM and Birks′ scheme are based on physical principles that contradict each other on the fundamental level, the excellent agreement obtained between both analyses first with polystyrene (Figure 2)42,55 and later with poly(Nisopropylacrylamide)41 was unexpected. Indeed, the FBM suggests that an excited pyrene probes a subvolume of the polymer coil whereas Birks′ scheme analysis of the fluorescence decays acquired with pyrene end-labeled polymers2,26,27,38,41,55 backed by theoretical work24,25 assumes that, as the polymer chain length increases, all excited pyrenes continue to probe the entire polymer coil. Although the use of Birks′ scheme analysis has been vindicated by a large body of studies dealing with short chains,2,26,27,38,41,55 work from this laboratory carried out with a series of monodisperse poly(ethylene oxide)s (PEO) end-labeled with 1-pyrenemethoxy groups (PEO-Py2) demonstrated that Birks′ scheme analysis breaks down for long polymers end labeled with pyrene.34 As the PEO chain length and solution viscosity increased, an increasing fraction of chains was found to be unable to form excimers, as would be expected if an excited pyrene were to probe the same subvolume (i.e., a blob) of a polymer coil whose dimensions increased with chain length. Furthermore, the set of parameters describing the 6533


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The study of the process of excimer formation inside micelles made of a pyrene-labeled gemini surfactant43 represented another example where the local distribution of pyrene labels was unsuited to apply the FBM3 or Birks′ scheme.2 The surfactant was a member of the N,N-bis(dimethylalkyl)-α,ωalkanediammonium dibromide family, where one of the two hydrophobic tails was replaced with a 1-pyrenehexyl substituent, the other was a dodecyl chain, and the ammonium head groups were separated by a propyl spacer.6 Because of its chemical composition, the surfactant was referred to as Py-3-12. The study of the micellization of Py-3-12 required the monitoring of the kinetics of excimer formation by steadystate and time-resolved fluorescence as a function of Py-3-12 concentration. One complication with such a study is the large solution absorbance obtained at high Py-3-12 concentration, which complicates the interpretation of the fluorescence spectra because of the inner filter effect.47 Fortunately, time-resolved fluorescence measurements are much less prone to this artifact, and MF analysis of the pyrene monomer and excimer fluorescence decays yielded all of the parameters needed to calculate the (IE/IM)SPC ratio with eq 8 as a function of SDS concentration. The rate constant ⟨k⟩ of excimer formation inside the Py-3-12 micelles was found to equal 79.2 ± 2.3 × 107 s−1, a very large value that was similar to the ⟨k⟩ value of Py16G4 in Figure 3 and reflected the large local concentration of pyrene units inside the Py-3-12 micelles as well as the relative fluidity of the micellar interior. An inspection of the molar fraction of pyrene units that formed the excimer by diffusion ( fdiff) indicated that excimer formation occurred mostly by diffusion despite the very large local pyrene concentration inside the Py-3-12 micelles. Multiplying the overall Py-3-12 concentration by the molar fraction of pyrenes that did not form the excimer (f free) yielded the concentration of free Py-312 monomers ([Py]free) that were not incorporated inside the micelles. As the overall Py-3-12 concentration increased, [Py]free increased until it plateaued at a [Py]free value of 0.22 mM (Figure 4). Interestingly, the value of [Py]free in the plateau region equaled the critical micelle concentration (cmc) of Py-312 in water as determined by surface tension and conductivity measurements.6 This study represented the first example in the literature where an analysis of the fluorescence decays acquired with solutions of a pyrene-labeled surfactant yielded the actual

Figure 3. Plot of the function (2G − 1)/G3 and ⟨k⟩ (×) obtained for the four pyrene-labeled poly(2,2-bis(hydroxymethyl)-propionic acid) dendrimers as a function of the generation number.

generation number, assuming that each pyrene group could probe the entire dendrimer volume. Because [Py]loc equals the number of pyrene groups in the ground state, which equals 2G − 1 (where G is the generation number) divided by the dendrimer volume that increases as Gα with α taking values between 1.5 and 3.3 depending on the dendritic construct,4 [Py]loc was expected to scale as (2G − 1)/Gα. Interestingly, the ratio (2G − 1)/Gα does not increase with increasing generation SPC number as was observed for (IE/IM)free=0 and ⟨k⟩ obtained with the pyrene-labeled dendrimers with 1 ≤ G ≤ 4. (See Figure 3 with α = 3.0.) This led to the conclusion that the pyrene end groups could not probe the entire dendrimer volume and were sequestered in a restricted domain of the dendrimer.39 As pointed out in a recent review,4 it was also the first time that the simple trend shown in Figure 3 between ⟨k⟩ and the generation number was found for a series of pyrene-labeled dendrimers. The extreme sensitivity of the (IE/IM)SS ratio to the presence of the free pyrene label was demonstrated for the pyrenelabeled dendrimers.9 Known amounts of 1-pyrenebutanol (PyBuOH) were added to a solution of Py 16 -G4 in tetrahydrofuran, and the steady-state fluorescence spectra and the pyrene monomer and excimer fluorescence decays of these mixtures were acquired. As increasing amounts of PyBuOH were added, the (IE/IM)SS ratio calculated from the fluorescence spectra decreased continuously. MF analysis of the fluorescence decays yielded the molar fraction of unattached pyrene labels, f free, which closely matched the molar fraction corresponding to the added free PyBuOH. The (IE/IM)SPC ratio decreased with increasing PyBuOH content in a manner similar to that of the SPC and ⟨k⟩ values that (IE/IM)SS ratio. However, (IE/IM)free=0 reflect the efficiency of pyrene excimer formation by diffusion were found to remain constant as a function of PyBuOH concentration because the presence of free PyBuOH does not affect pyrene excimer formation at the low pyrene concentration (2.5 μM) used in these experiments. These experiments demonstrated the ability of the analysis programs to retrieve quantitatively the molar fractions of the pyrene species present SPC in solution as well as the parameters (IE/IM)free=0 and ⟨k⟩ describing the efficiency of the pyrene excimer formation process.

Figure 4. Plot of the concentration of the free Py-3-12 gemini surfactant ([Py]free) as a function of the total Py-3-12 concentration. [Py]free plateaus at the cmc of Py-3-12. 6534


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cmc of the surfactant. It also demonstrated the ability of the analyses conducted in this laboratory to determine quantitatively and accurately the molar fractions of the various pyrene species in solution. Study of Pyrene Aggregates in Water. Because of their low level of hydrophobic modification, hydrophobically modified water-soluble polymers (HMWSPs) remain soluble in water but associate intermolecularly to form a polymeric network held together by physical interactions between the hydrophobes.63,64 As a result of network formation, the viscosity of the HMWSP aqueous solution is strongly enhanced but the application of a shear to the HMWSP solution distorts the network in a way that can lead to shear thickening or shear thinning of the solution. The addition of a surfactant to an HMWSP solution affects the polymeric network, which can result in dramatic viscosity enhancements of the solution.65 Because the peculiar viscoelastic properties of HMWSP solutions are a result of hydrophobic associations, the hydrophobes of HMWSPs have been replaced in a large number of studies by hydrophobic pyrenyl pendants to yield Py-HMWSPs, which are used to investigate by fluorescence how the hydrophobes contribute to the rheological behavior of a Py-HMWSP solution.5 The suite of programs developed in this laboratory lends itself easily to the determination of the level of pyrene association by determining the molar fractions of pyrene species that are preassociated in the ground state, namely, fagg = f E0 + f D. One surprising observation was that not all pyrene hydrophobes were aggregated in aqueous solutions of the PyHMWSPs. In the case of a series of water-soluble poly(N,Ndimethylacrylamide)s randomly labeled with pyrene, the level of pyrene aggregation was found to increase with increasing pyrene content of the Py-HMWSP.45 Adding a surfactant to an aqueous solution of pyrene-labeled, hydrophobically modified, alkali-swellable copolymer (Py-HASE) led to a decrease in the level of pyrene aggregation, which could be easily tracked by a global analysis of the fluorescence decays to retrieve fagg.66 PyHASEs are the fluorescent analogues of a commercially important family of associative thickeners. The addition of SDS melted the pyrene aggregates, which could be followed by monitoring (IE/IM)SS as a function of SDS concentration, and the solution viscosity was found to increase, pass through a maximum, and decrease (Figure 5).67 Although this effect is typical of mixtures of nonfluorescent HASEs and surfactant, a global analysis of the fluorescence decays with the FBM yielded the average number of pyrenes per SDS micelle (⟨n⟩). In this case, the immaterial blobs became the well-defined SDS micelles. Increasing the SDS concentration led to the formation of more SDS micelles, which was accompanied by a decrease in ⟨n⟩ as the pyrene groups distributed themselves among an increasing number of SDS micelles. Interestingly, (IE/IM)SS and the solution viscosity did not reach a maximum value at the same SDS concentration in Figure 5 because diffusional excimer formation with a large ⟨n⟩ value maximizes (IE/IM)SS whereas solution viscosity is maximized by a most efficient network. The combination of fluorescence and rheology experiments revealed that the solution corresponding to the maximum viscosity had an average number of pyrenes per hydrophobic junction equal to 2.0 in Figure 5, the value expected to obtain the most efficient network.67 The retrieval of the molar fractions related to the different pyrene species in solution through the global analysis of the

Figure 5. Plot of (○, top panel) ⟨n⟩, (□) (IE/IM)SS, and (■, η) solution viscosity as a function of SDS concentration.67

fluorescence decays of a given pyrene-labeled macromolecule was also instrumental in determining for the first time the fluorescence quantum yield and the molar absorbance coefficient of pyrene aggregates generated in aqueous solutions of Py-HMWSPs. Pyrene aggregates in water were found to absorb 1.7 times more than the pyrene monomer at the S20 ← S00 band68 and emitted light 4.5 times less efficiently than did the pyrene excimer in organic solvents,69 a conclusion that had been suggested earlier on the basis of data obtained with different Py-HMWSPs.70−72 Pyrene-labeled lipids (Py-LL) have also been prepared with a metal recognition site.7 In the absence of metal cations in solution, 1 mol % Py-LL forms Py-LL aggregates in the lipid membrane made of 1-palmitoyl-2-oleyl-3-sn-phosphatidylcholine (POPC) or distearylphosphatidylcholine (DSPC), and excimer fluorescence is observed. Upon addition of lanthanum cations (La3+), the binding of La3+ to Py-LL results in a decrease in excimer emission, which was originally attributed to the break up of the Py-LL aggregates resulting from electrostatic repulsion. In fact, the determination of the molar fractions of the different pyrene species in solution indicated that fagg did not change upon La3+ binding but that fdiff decreased while f free increased.73 This observation led to the conclusion that the decrease in excimer emission was not due to the break up of the Py-LL aggregates but rather to the decrease in excimer formation by diffusion between isolated PyLL in the lipid membrane resulting from electrostatic repulsion between the bound La3+ cations. This study provided information on how metal cations such as La3+ bind to specific lipids in membrane bilayers.

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FUTURE RESEARCH This article has demonstrated that quantitative information could be retrieved about the internal dynamics of linear chains,3,34,41,42,46,52−60 polymer aggregates,35,40,45,66−69 dendrimers,4,9,39 micelles made of gemini surfactants,43 and lipid bilayers73 by characterizing the process of excimer formation between pyrene labels covalently attached to these macromolecules. Together, this ensemble of studies suggests that, if 6535


Langmuir the proper measures are taken to ensure that the analysis of the monomer and excimer fluorescence decays is properly conducted, quantitative information on the internal dynamics of any macromolecule can be gained as long as it is labeled with at least two pyrene moieties that can form excimer dynamically. The battery of new analytical tools presented in this review leads to questions concerning what new scientific challenges could be addressed by applying such tools. The first challenge on the author’s list would be the characterization of the internal dynamics of dendrimers. Because the mass of a dendrimer increases faster with increasing generation number than its volume, a point is reached during the growth of a dendrimer where all free volume in the interior of the dendrimer disappears.74 This unavoidable conclusion has led many scientists to investigate theoretically and experimentally the location of the dendrimer terminals because their activity, which is critical to numerous applications pertaining to dendrimers, is maximized when the terminals reside near the dendrimer surface.62 However, the location of the dendrimer terminals might be less relevant than their dynamics because fast dynamics would enable the dendrimer ends to be shuttled quickly back and forth from the dendrimer interior to its periphery, regardless of their position within the dendrimer. Probing the dynamics of a dendrimer’s terminals can be done by monitoring the process of excimer formation between the pyrene-labeled ends as a function of dendrimer generation. Unfortunately, this straightforward experiment has been conducted on only a handful of occasions and, as a recent review on the topic argues,4 has led to rather inconclusive results. Certainly, the possibilities brought to the forefront by the new analytical tools presented in this review suggest that it would be worthwhile to revisit these experiments. Another research venue that might take advantage of these tools would establish a flexibility scale of short amino acid sequences. By dividing a given protein sequence into snippets of tripeptides or tetrapeptides that could be polymerized into polypeptides with well-defined sequences,75 the pyrene labeling of these polypeptides would enable the characterization of the flexibility conferred to a polypeptide by a given repeating sequence of amino acids. In turn, this information would prove valuable in describing the folding pathway of a protein, which must depend on the relative flexibility of the stretches of amino acids constituting its sequence. One important impediment to such a project, however, is the insolubility of pyrene in aqueous solutions. Because many proteins are water-soluble, the previous study would be facilitated if a noncharged, water-soluble pyrene analogue existed because pyrene is best suited to studying the internal dynamics of macromolecules that dissolve in organic solvents. Unfortunately, the hydrophobicity of pyrene becomes a curse in studying the dynamics of polar water-soluble macromolecules that do not dissolve in dimethylsulfoxide or N,Ndimethylformamide. To be useful, a water-soluble pyrene analogue would need to have a long lifetime to probe the slow internal dynamics of macromolecules, be noncharged to avoid specific electrostatic interactions with charged macromolecules, and form an excimer so that a single labeling step of the macromolecule is required and a global analysis of the monomer and excimer fluorescence decays can be accomplished.

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CONCLUSIONS

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AUTHOR INFORMATION


Over the past 15 years, improvements in the analysis of fluorescence decays of pyrene-labeled macromolecules have enabled the quantitative study of the kinetics of pyrene excimer formation of a remarkably diverse range of macromolecular architectures and properties. As this review suggests, macromolecules need no longer be pyrene-labeled at only two specific positions, and thanks to the MF analysis, quantitative information about the properties of a macromolecule can be obtained even if a fully descriptive model is not available. In using pyrene excimer formation to study the internal dynamics of macromolecules and their assemblies, work reviewed in this report has illustrated how polymers, self-associating watersoluble polymers, end-labeled dendrimers, surfactants, and lipids labeled with pyrenyl groups can now be probed routinely through the quantitative analysis of their fluorescence decays. These early results suggest that time-resolved fluorescence can now be used in a quantitative manner to probe any type of pyrene-labeled macromolecule.

Notes

The author declares no competing financial interest.

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REFERENCES

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